Monday 11 July 2011 12.19 EDT
First published on Monday 11 July 2011 12.19 EDT

The family of the murdered schoolgirl Milly Dowler has called for Rebekah Brooks to resign over allegations that News of the World journalists paid a private investigator to hack into her phone while she was missing.

The family's lawyer said Brooks, the chief executive of Rupert Murdoch's News International, who was editor of the News of the World at the time the hacking took place, should "do the honourable thing" and go.

A statement read out by Mark Lewis on the steps of the Cabinet Office, after a 50-minute meeting with Nick Clegg, said: "They [the Dowler family] believe it is vital that the people responsible be held to account. There are very senior people who have to take responsibility for what happened in their media organisation."

The statement leaves it open for the family to push for people even higher up the Murdoch hierarchy to take responsibility for the problems at the paper.

He added that Brooks should "do the honourable thing" and go, saying: "They don't see why she should stay in the job. They see this as something that went right to the top. She was editor of the News of the World at the time that Milly was taken in 2002. She should take editorial responsibility."

Last week's Guardian revelation that 13-year-old Milly's phone was allegedly hacked in the days and weeks after she went missing, and that the hacker deleted messages when her mailbox was full, giving the family false hope that she was alive [see footnote], sparked the furore about journalistic practices at News International.

Milly's mother, Sally, 51, told Clegg the family had only learned about the alleged hacking of Milly's voicemail just before the trial of her killer, Levi Bellfield.

The Dowlers were joined by members of Hacked Off, a new campaign formed to ensure the victims of hacking get justice. Members at the meeting included the former Scotland Yard deputy assistant commissioner Brian Paddick, whose phone was also allegedly hacked, the director of the Media Standards Trust, Martin Moore, and the former Lib Dem MP Evan Harris.

On Monday there were also claims in the Mirror, which could not be substantiated by the Guardian, that a former New York police officer said he had been contacted by News of the World journalists in the wake of 9/11. The ex-officer, whose identity is not known, is said to have claimed reporters offered to pay him to retrieve the private phone records of the dead.

Celebrities who are also said to be hacking victims have launched a ferocious attack on the newspaper. In an extraordinary appearance on BBC2's Newsnight on Friday, comedian Steve Coogan said the paper's closure was "a wonderful day for the press: a small victory for decency and humanity".

He said: "People talk as if they have fallen below their usual high standards. They were already in the gutter. It is just that they have sunk lower than anyone thought they could."

The actor Hugh Grant has regularly attacked the News of the World, saying people felt "viscerally sickened" by the Milly Dowler allegations.

The musician George Michael has also condemned the newspaper in a series of tweets, describing its closure as "a fantastic day for Britain". In a cryptic update on Monday he wrote: "just spoke to my lawyer … apparently they want to interview me about my comments on Rebekah Brooks here on twitter."

• The following was published on 12 December 2011 in the corrections and clarifications column: An article about the investigation into the abduction and death of Milly Dowler (News of the World hacked Milly Dowler's phone during police hunt, 5 July, page 1) stated that voicemail "messages were deleted by [NoW] journalists in the first few days after Milly's disappearance in order to free up space for more messages. As a result friends and relatives of Milly concluded wrongly that she might still be alive." Since this story was published new evidence – as reported in the Guardian of 10 December – has led the Metropolitan police to believe that this was unlikely to have been correct and that while the News of the World hacked Milly Dowler's phone the newspaper is unlikely to have been responsible for the deletion of a set of voicemails from the phone that caused her parents to have false hopes that she was alive, according to a Metropolitan police statement made to the Leveson inquiry on 12 December.